Self-Similar Inverse Semigroups from Wieler Solenoids
- 주제(키워드) Smale space , Wieler solenoid , self-similar inverse semigroup , limit solenoid , groupoid of germs , tight groupoid , unstable C-algebra
- 주제(기타) Mathematics
- 설명문(일반) [Yi, Inhyeop] Ewha Womans Univ, Dept Math Educ, Seoul 03760, South Korea
- 등재 SCIE, SCOPUS
- OA유형 gold, Green Submitted
- 발행기관 MDPI
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000168825
- 본문언어 영어
- Published As https://dx.doi.org/10.3390/math8020266
초록/요약
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs and the tight groupoids of these inverse semigroups are equivalent to the unstable groupoids of Wieler solenoids. We also show that the <mml:semantics>C</mml:semantics>-algebras of the groupoids of germs have a unique tracial state.
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